Question 1188743: The sum of two numbers is 33. The sum of the squares of these numbers is 557. Find the two numbers.
Answer by VFBundy(438)   (Show Source):
You can put this solution on YOUR website! Make two equations:
x + y = 33
x² + y² = 557
From the first equation, let: y = 33 - x
Substitute y = 33 - x into the second equation:
x² + (33 - x)² = 557
Simplify and solve for x:
x² + (1089 - 66x + x²) = 557
2x² - 66x + 1089 = 557
2x² - 66x + 532 = 0
x² - 33x + 266 = 0
(x - 14)(x - 19) = 0
x = 14; x = 19
There are two solutions. If you let x = 14 and substitute this into the original first equation (x + y = 33), this means y = 19.
And, if you let x = 19 and substitute this into the original first equation (x + y = 33), this means y = 14.
Either way, the two numbers you are looking for are 14 and 19.
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